BK10110302-Shuler Problems.pdf

V.Prasarnth Raaj Shuler Problems BK10110302

SOLUTIONS

Problem 3.12

1. Is Harry’s reasoning right? Do you agree with him?

Harry’s reasoning is right. Immobilization often prolongs the life of the protein. Thus I

agree with Harry that, immobilization can prolong the active lifespan of enzymes (although

it can also kill enzyme with certain linkages).

2. Why is that so?

Aggregation is often a problem with proteins in solution, the higher the concentration of

enzyme, the quicker the aggregation and it can lead the enzymes to die faster. This can

be further increased if redox sites are involved, at least in part due to cysteine reactivity

and divalent bonds forming between enzymes leading to inactive sludge Additionally,

enzymes which undergo conformational changes during their catalysis also can become

more prone to denature in a purified state denatured proteins also tend to glom up more

readily, rendering dead enzyme quite quickly. Certain enzymes (those designed to chew

up other molecules) also will exhibit some activity against themselves (even if low, this

adds up quickly in the high concentration, low other-substrate type environment of

storage). Immobilization solves several of these problems - enzymes are at a relatively

low concentration for aggregation and inter-enzyme reactions with each other, while they

can still be at a high relative concentration of reaction with substrate flowed through the

beads. From the description the type of beads is Poros-type beads


Problem 3.14

a. Because the reaction rate is almost the same for the 0.1 and 0.2 cm particle diameter, we

can assume that the rate of reaction without immobilizing uricase enzyme is 200 mg l-1 h-

1.

∴ 𝜂(Dp = 0.5cm) =100

200= 0.5

𝜂(Dp = 0.7cm) =50

200= 0.25

b. Applying Lineweaver-Burk plot,

1

𝑣=

1

𝑉𝑚+

𝐾𝑚

𝑉𝑚

1

[𝑆]

𝑆0(mg UA ∙ 𝑙−1) 1/𝑆0 𝑣 (mg UA ∙ 𝑙−1 ∙ h−1) 1/𝑣

10 0.1 10 0.1

25 0.04 20 0.05

50 0.02 30 0.033333

100 0.01 40 0.025

200 0.005 45 0.022222

250 0.004 46 0.021739

𝑉𝑚 =1

0.017= 58.82 mg UA ∙ 𝑙−1 ∙ h−1

𝐾𝑚 = 0.821 × 58.82 = 48.29 mg UA ∙ 𝑙−1

y = 0.8217x + 0.0175

0

0.02

0.04

0.06

0.08

0.1

0.12

-0.03 -0.01 0.01 0.03 0.05 0.07 0.09 0.11

1/v

1/S

Lineweaver-Burk Plot


Problem 3.15

a.

d=2mm ; r=1mm

[Sb]=0.5mM ; neglect liquid film resistance, therefore [Sb]= [Ss]

v=10mM h-1 = 2.78x10-3mM s-1

De=1.5x10-5cm2/sec

Km' = 0.2 mM

𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑠𝑝ℎ𝑒𝑟𝑒 =4

3𝜋𝑟3

𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑠𝑝ℎ𝑒𝑟𝑒 = 4.18 × 10−3𝑐𝑚3

𝑟𝑎𝑡𝑒 𝑜𝑓𝑢𝑟𝑒𝑎 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠, 𝑣 =2.78 × 10−3𝑚𝑀𝑠−1

4.18 × 10−3𝑐𝑚3

𝑣 = 0.665𝑚𝑀 𝑐𝑚−3𝑠−1

𝑣 =𝑉𝑚[𝑆𝑠]

𝑘𝑚 + [𝑆𝑠]

0.665𝑚𝑀 𝑐𝑚−3𝑠−1 =(𝑉𝑚)(0.5𝑚𝑀)

0.2𝑚𝑀 + 0.5𝑚𝑀

𝑉𝑚 = 0.931𝑚𝑀 𝑐𝑚−3𝑠−1

𝜙 = 𝑅√𝑉𝑚 𝑘𝑚⁄

𝐷𝑒𝜙 = 0.1𝑐𝑚√

0.931𝑚𝑀 𝑐𝑚−3𝑠−1 0.2𝑚𝑀⁄

1.5 × 10−5𝑐𝑚2𝑠−1

𝜙 = 55.7

ɳ =3

𝜙

ɳ =3

55.7

ɳ = 0.0538

b.

d=4mm ; r=2mm ; r=0.2cm

𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑠𝑝ℎ𝑒𝑟𝑒 =4

3𝜋𝑟3

𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑠𝑝ℎ𝑒𝑟𝑒 = 0.034𝑐𝑚3


𝑟𝑎𝑡𝑒 𝑜𝑓𝑢𝑟𝑒𝑎 ℎ𝑦𝑑𝑟𝑜𝑙𝑦𝑠𝑖𝑠, 𝑣 =2.78 × 10−3𝑚𝑀𝑠−1

0.034𝑐𝑚3

𝑣 = 0.082𝑚𝑀 𝑐𝑚−3𝑠−1

𝑣 =𝑉𝑚[𝑆𝑠]

𝑘𝑚 + [𝑆𝑠]

0.082𝑚𝑀 𝑐𝑚−3𝑠−1 =(𝑉𝑚)(0.5𝑚𝑀)

0.2𝑚𝑀 + 0.5𝑚𝑀

𝑉𝑚 = 0.1148𝑚𝑀 𝑐𝑚−3𝑠−1

𝜙 = 𝑅√𝑉𝑚 𝑘𝑚⁄

𝐷𝑒𝜙 = 0.2𝑐𝑚√

0.1148𝑚𝑀 𝑐𝑚−3𝑠−1 0.2𝑚𝑀⁄

1.5 × 10−5𝑐𝑚2𝑠−1

𝜙 = 39.12

ɳ =3

𝜙

ɳ =3

39.12

ɳ = 0.0767


Problem 3.17


Problem 3.18


Problem 6.15 (a)


Problem 6.15 (b)


Problem 6.17


Problem 6.17


Problem 6.19 (a)


Problem 6.19 (b)

Two graph need to be plotted in order to find the optimum dilution rate

Plot 1

DX vs D

Plot the table below using this equation

DX = 0.1-((0.004*D)/(0.2-D))

D DX

40 0.10402

30 0.104027

20 0.10404

10 0.104082

0 0.1

Optimum dilution rate maximizing productivity of biomass, Dopt = 12.5

0.0995

0.1

0.1005

0.101

0.1015

0.102

0.1025

0.103

0.1035

0.104

0.1045

0.105

0 5 10 15 20 25 30 35 40 45

Pro

du

ctiv

ity

of

Bio

mas

s, D

X

Dilution Rate, D

DX vs D

12.5


Plot 2

DP vs D

Plot the table below using this equation

DP = 0.2-((0.008*D)/(0.2-D))

D DP

0 0.2

20 0.208081

40 0.20804

60 0.208027

80 0.20802

Optimum dilution rate maximizing productivity of product, Dopt = 25

0.199

0.2

0.201

0.202

0.203

0.204

0.205

0.206

0.207

0.208

0.209

0.21

0 10 20 30 40 50 60 70 80 90

Pro

du

ctiv

ity

of

Pro

du

ct, D

P

Dilution Rate, D

DP vs D

25

BK10110302-Shuler Problems.pdf

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BK10110302-Shuler Problems.pdf